Is this a conjugate match network?

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triquent

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For an impedance z=35-j28ohms(z'=0.7-j0.56), design matching networks(to 50ohm). Then looking towards the generator(which is assumed to have an impedance of 50ohms), this provides z=35+j28ohms(z'=0.7+j0.56). This proves the conjugate match technique.
My question is:: are all of matching networks conjugate matching network? I found some matching network is conjugate and some are not.

for example:
1) using serial L(X'=j1.01) and shunt C(B'=j0.65) got matching network is a conjugate matching network.
2) using serial L(X'=j0.56) and serial R(Z'=0.3), then this matching network is not a conjugate matching network. This matching network 's impedance is 1.3+j0.56.

But the professor in the class said all of it should be a conjugate matching network. why my calculation didn't prove it?
 

Theory says that you can cut a discrete element network that matches two impedances to each other and the impedance looking both directions are the conjugate of each other.

You can do a thought experiment on this. If they were not, there would be a reflection of power at that point.
 

I think I see your problem. When your professor says to you "the best matching network is a conjugate match", what he really means to say is "the best match that optimizes power transfer to the load is a lossless conjugate matching network".

If I had a 10 ohm load, that I was trying to match to a 50 ohm source, one could obviously "match" this by using 40 ohm series resistor. The reflection coefficient would be zero, and you would have a perfect match. Unfortunately, most of the power will be dissipated into the "matching network" as heat, instead of getting into the load where it will do the most good. So from a power transfer point of view, it was a lousy match!

Stick to lossless matching networks for most applications. The only exceptions to this is where you have to provide some lossy match for stability reasons, or where you have RF power to burn!
 

The professor think any matching network will be conjugate. But I found with resistance(lossy network) it is not conjugate. so i am wondering weather that conjugate theory is only right for the lossless network?
To design the maximum gain amplifier, we need to design the conjugate matching network. Then this means we only can use the lossless network(L,C)?

 

Yes, you should use L's, C's, and transmission line sections for the match. Do not deliberately use resistors. But you should realize that any real world element has some loss, and to be thorough you should include that loss in your analysis. The L's and C's should be modeled with a realistic Q (inductor Q=40, capacitor Q=200 for example), and the tranmission lines modeled with a realistic loss per length.

Often, especially when you try to do a very narrowband match, or a big impedance transformation, that small loss suddenly has a big effect.
 

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